'I ­always seek higher ground. I do want to be part of great things' … Patricia Clarkson in The East. Photograph: Daniel Scott

When I told an actor friend I was interviewing Patricia Clarkson, she yelled: "Oh my god, she's the best thing about every film she's in!" My friend, who is in her 30s, added: "Tell her I want to be her when I grow up."

This seems to be how lots of people feel about Clarkson. She may be an actors' actor, a woman who steals just about every scene she's in, but she's also adored by anyone who's ever watched Six Feet Under and felt a thrill whenever she cropped up as the slightly unhinged hippy Aunt Sarah, or wished Woody Allen had cast her as something more than a peripheral relative in Vicky Cristina Barcelona.

Her screen idol is, she says, Tallulah Bankhead, the flamboyant, fast-living star of American stage and screen famed for being able to put away a bottle of bourbon in 30 minutes. The way Clarkson describes her is, I think, the way the rest of the world might describe Clarkson (or at least the first part is): "She's a person we all want to know, we all want to have sex with – and drinks with – maybe simultaneously."

I have half an hour with her in a Manhattan hotel room, but her easy expansiveness – arms flung wide, wrists dangling – makes me feel as though we're on some Louisiana porch, drinking Long Island iced tea as the sun sets. There's a sly mischief to her, too: she looks as if she's keeping a naughty secret that she might just share with you later, an impression helped along by that famous voice – low, throaty and stretched long with southern vowels. If she didn't exist, Tennessee Williams would have had to invent her.

As she starts talking about her new film, a thriller called The East written by young director Zal Batmanglij and co-starring Brit Marling, she makes some grand pronouncements: "I always seek higher ground. I do want to be part of great things, whether leading or supporting." When she gets lofty, she stammers, brimming with passion. It's a performance, perhaps, but it's still irresistible.

Clarkson plays Sharon, the serenely amoral head of a private intelligence firm that tasks Marling's character with infiltrating The East, an anarchist eco-terrorist group. Did the film change any of her political convictions? "No, it enforced everything I feel," she says. "That's what was fabulous about Sharon. I like playing people who are antithetical to me."

In one of the film's most intense moments, Marling grabs an apple core from a bin and eats it before Clarkson, in an extreme demonstration of freeganism. "In that moment comes the realisation that maybe I haven't had the upper hand all along," she says. "That I did not completely destroy her moral compass – mine is gone, but she still has one. Which is the biggest pow, the biggest kick to the gut you can have: to see in someone else what is so sorely lacking in yourself."

Clarkson, now 53, was born in New Orleans, the youngest of six daughters. Her parents ("Married 60 years and still together – and still alive!") remain pillars of the community. Her mother is president of the city council and her father was a school administrator. Following her studies at Yale, Clarkson has had a steady film and TV career since the 1990s. And, from The Untouchables to Far From Heaven to Six Feet Under, there's not an embarrassment among them: she clearly chooses judiciously.

"I'm picky at times," she says. "I have sometimes tried to battle the system by saying no to parts I found unbearable. Parts that are desexed, matronly – to just put me in a couple of scenes and have me be the older, you know, dead character, is not gonna fly with me. But I'd say more doors have opened as I've gotten older, which is what you want. It's when all the doors start to slam that I get sad for women my age. Because it's wrooonnng."

She delivers that last word with a kind of oratorical vibrato. Suddenly you understand why, when she was just 13, a teacher decreed that she was already an actor. "I've had my moments when silence was not an option, you know?" she smiles. Foremost among them was the time she spoke at the 2009 Human Rights Campaign Gala in favour of gay marriage. "I'm not a gay woman, but it doesn't matter – you have to rise to the occasion when you're called upon. I'm passionate and feisty and mercurial," she laughs, "but I'm opinionated and political. It's just who I am, just how I was raised."

Her breakout role came in 1998, with then first-time director Lisa Cholodenko's High Art, in which Clarkson played Greta, a ravaged yet glamorous heroin addict. Since then, she's made a habit of working with young or first-time directors. "I sometimes feel I'm underpaid," she says. "And sometimes I get a very nice paycheck and I am thankful. But this business wears women down. It has to – the percentage of roles for women is dramatically less. But there are parts, and the rise of independent film has changed the landscape for women – it gave me a career."

That said, Clarkson does enjoy doing big studio films. "I'd love to play an action hero!" she says. "Even a kick-ass mother of an action hero. Put me in a black latex suit, c'mon! Just give me a couple of weeks to do some sit-ups." Her laughter is the only kind I've ever heard that actually deserves the word "peals": she reels in her seat with it.

When she's recovered, I ask if she is in any way glad not to have reached the leading-woman A-list stratosphere. "No, no, that would be false modesty," she says. "Being a big star is a very, very good thing. More doors open, it's easier to get a film made. I've tried for eight years to get one made, and we're finally doing it. It's a beautiful film called Learning to Drive and it stars me and Ben Kingsley and it's delicious and yummy and funny, funny, funny, and very moving."

She feels she's more ready than ever to play the part. "Because we get better as actors, we really do. Who you are is always at the core of the character you create: you can never fully divest yourself from yourself. The greatest characters we create, the greatest moments of art or craftsmanship we are able to have come from a place of self-worth."

That doesn't seem something she's short of. It shouldn't be anyone's business but hers, but it is striking that she's never married. Is that, I ask tentatively, a deliberate choice? "No, it's not deliberate," she says evenly. "Don't get me wrong, I hate being single. I've had beautiful, extraordinary men in my life and I wouldn't change any of that. But I've never wanted to marry, I've never wanted children – I was born without that gene."

So are there no men in her life? "I date," she says. "Not as much as I should, to be honest. I love being in love – I'm a moth to a flame. It is, I think, the reason we're here."